Efficient linear-quadratic filtering

We present two approaches to efficient linear-quadratic (LQ) filtering. The first of these is implemented in the frequency domain and requires less computations than the second (time domain) approach. The savings are similar to those obtained by executing linear filtering in the frequency domain with the use of the Fast Fourier Transform (FFT). The one drawback of the frequency domain method is the delay that is induced that is related to FFT length. A time domain method that does not suffer from this delay problem is subsequently derived. Our time domain approach involves rearranging the LQ filtering structure so that the quadratic part of the system consists of a bank of linear filters that can be run in parallel. The inputs to these linear filters are products of the original input signal